Question

When performing a hypothesis test on proportions (either where H0: p = p0 or where H0: p1 = p2)you should use the observed number of successes and failures when checking conditions

a) True

b) False

c)Depends on the context

c)Observed proportion for one sample, expected proportion for two samples

Answer 1

When conducting one sample hypothesis test on proportions, the condition to be checked is that $np_0 \space and \space n(1-p_0)\geqslant 10$ where $p_0$ is the null value and $n$ is the sample size. $np_0$ is the expected number based on the null proportion.

For a two sample hypothesis test a common estimator for $p$ is used. The estimator for $p$ is given as, $\hat{p}=(x_1+x_2)/(n_1+n_2)$ where $x_1\space and \space x_2$ are the number of successes for population 1 and 2 respectively. $n_1\space and \space n_2$ are the sample sizes for population 1 and 2 respectively. The condition to be checked is $n_1\hat{p}\space and \space n_1(1-\hat{p})\geqslant 5$, and $n_2\hat{p}\space and \space n_2(1-\hat{p})\geqslant 5$. In any case, the number of successes and failures are not used to check the conditions.

However, the number of successes and failures are used when finding a confidence interval for the population proportion.

Therefore, b) false, is the correct choice.